Abgeschlossene Arbeiten
Gruppen Bluhm DiVincenzo Hassler Müller Terhal
Gruppe Bluhm
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Urheberrecht: © Simon SchaalB.Sc.Arbeit Long Range
Coupling between Spin Qubits
The Double Quantum Dot system in GaAs can be used for quantum information processing. This thesis benchmarks different ways to couple several qubits to enable good multiqubit operations.
Dokument (PDF)
M.Sc.Arbeit Nuclear Spin Mediated LandauZener Transitions in Double Quantum Dots
The Double Quantum Dot system in GaAs is a promising hardware for quantum information processing. In this thesis, a measurement scheme to probe the dynamics of nuclear spins in GaAs quantum dots is presented. Dokument (PDF)
Urheberrecht: © Pascal CerfontaineM.Sc.Arbeit HighFidelity Qubit Gates for TwoElectron Spin Qubits
Highfidelity gate operations for manipulating qubits in the presence of decoherence are a prerequisite for faulttolerant quantum information processing. This work theoretically develops control pulses for singlettriplet qubits in GaAs double quantum dots with fidelities as high as 99.9%.
Dokument (PDF)
M.Sc.Arbeit Probing Classical and QuantumMechanical Baths with a Qubit
The investigation of deleterious interactions between a qubit and its environment is important for quantum information research. In this thesis, techniques using qubit evolution and readout to investigate interactions with both classical and quantummechanical noise baths are introduced.
Dokument (PDF)
Gruppe DiVincenzo
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B.Sc.Arbeiten

Sebastian Issel: Blackbox and Whitebox Algorithms for Efficient Parallel Quantum Computation

Pia Döring: Quantum Cryptography with Microwaves

Jan Alexander Herbort: Strong Coupling between a Spin Qubit and a Resonator

Florian Nolte: Measuring noncommuting quantum operators

Dennis Huben: Geometric Layouts of Qubits for New Lattice Codes

Cedric Sodhi: Hall effect in an eightshaped conductor

Jens Bröder: Modelling of Electromagnetic Response of Cubical Cavities

Tobias Herrig: Approximation of the Relaxation Time of Nuclei in Silicon at Room Temperature

Benedikt Placke: RealWorld Quantum Hall Gyrators and Circulators

Martin Wosnitzka: Qbit Layouts for Quantum Computation Using NonAbelian Anyons

Yudai Suzuki: Multiport Impedance of the parity measurement network with Tunable Coupling Qubits
M.Sc.Project Beyond the rotating wave approximation dynamics of highfidelity quantum gates
In this thesis, using the effective Hamiltonian approach based on the Magnus expansion, the time evolution of highfidelity quantum gate for singlettriplet qubit is studied. A new approach for calculating such an effective Hamiltonian is presented. The goal of this new methodoloy is to find a nonrecursive formula for the effective Hamiltonian, thereby reducing the computational cost of determining such effective Hamiltonians. In the process of doing so, few simplifications are obtained as well as new directions for further development of the formalism is motivated. Thesis
Urheberrecht: © Rijul SachdevaM.Sc.Project Exploring remote quantum computation using Simon Algorithm within Blind Oracular Quantum Computation scheme
In this thesis, the concept of Universal blind quantum computation, in which a client with limited resources controls the execution of a quantum computation on a server without revealing any details of the computation, is developed. This idea is extended to a threenode setup used to carry out oracular quantum computation in a blind environment. In this Blind Oracular Quantum Computation(BOQC) scheme, there is the Oracle, with limited power along with the client to supply quantum information to the server so that the oracular part of the computation can also be carried out blindly. We develop tests of this protocol using Grover and Simon Algorithm. Thesis
Urheberrecht: © Jonathan ConradM.Sc.Project Tailoring GKP Error Correction to Real Noise
In the wake of recent experimental advances in high precision control of quantum harmonic oscillators, such as embedded in trapped ions or microwave cavities, the theme of this work is to analyze noise processes a particular bosonic quantum error correcting code, called the GKPCode, experiences in realistic scenarios, and to investigate how one can adapt decoding strategies to cope for such noise. To this end, this work presents analytical studies of error channels that perturb GKPencoded qubits, i.e. propagated finite squeezing (finite energy) errors and photon loss. It is shown, how one can use these results to derive tailored decoding strategies, which are then tested in numerical simulations. Furthermore, we discuss how one can implement and use machinelearning techniques to further adapt decoding strategies to hardware. Thesis
Urheberrecht: © Tobias HerrigM.Sc.Project Measurement Simulations of Coupled Qubits with QuTiP
The motivation for this thesis was to investigate if and how it is possible to realize a singlequbit measurement in a system of coupled qubits. The goal was to simulate a homodyne detection on a system with two coupled qubits and a readout resonator. Thesis
Urheberrecht: © Martin RymarzM.Sc.Project The Quantum Electrodynamics of Singular and Nonreciprocal Superconducting Circuits
This thesis deals with two systems in the field of circuit quantum electrodynamics. In the first part we extend a recently proposed singular superconducting circuit architecture that realizes a qubitresonator system with tunable coupling, in particular taming the circuit singularity. In the second part we introduce the gyrator into circuit quantum electrodynamics, discussing its quantization, its potential singularity and how to cancel it, as well as its nonreciprocity, which is furthermore studied with the aid of an example. Thesis
Urheberrecht: © Joel Christin PommereningM.Sc.Project Multiqubit Coupling Dynamics and the CrossResonance Gate
The crossresonance gate is implemented by applying a microwave drive to a system of two coupled qubits. I study the nonlocal properties of the driven and undriven system induced by this coupling. In the undriven case, entanglement is still being generated, but it is periodic and bounded linearly by the ratio of coupling strength and qubit frequency detuning. Specifically I derive an upper bound for the concur rence as a measure of entanglement. Dokument(PDF)
Urheberrecht: © Veit LangrockM.Sc.Project Numerical and theoretical investigation of longrange coherent electron shuttling devices in Silicon/SiliconGermanium quantum wells for scalable quantum computing
The aim of this thesis is to investigate what kind of problems currently envisioned coherent electron transfer devices may encounter in Silicon/Silicon Germanium gateconfined nano structures, and to lay out proper methods to de scribe them in a sufficiently efficient manner. Thesis
Urheberrecht: © Adrián Parra RodríguezM.Sc.Project Software Tool to Analyse Superconducting Qubits
This thesis is a description of the program “Superconducting Qubit GUI” that following the methods of existing literature, it helps automate ordinary electrical network graph theory in superconducting circuits.The main objective of the Superconducting Qubit GUI is to be as useful as possible to a researcher in the field. It is open to changes for improvement since the written code offers a nice interface for further development. Dokument
M.Sc.Arbeit Quantum Information Processing with Surface Acoustic Waves
Alan Salari
In the first part of the present work, I’m going to investigate the wave propagation in cubic piezoelectric crystals such as GaAs and also wave generation by interdigital transducers. In the second part, I propose and investigate the idea of looking at spiral IDTlike structures, which might permit the simultaneous coupling to two cavities in orthogonal directions. Using COMSOL simulations, I’ve calculated several parameters of the spiral transducer, such as its capacitance, input admittance and response function. The coupling rate of the spiral transducer has also been calculated using semiclassical model for the qubit.Moreover, I have studied the IDTtransmons of Delsing's group. The physics of this is rather different than in conventional "circuit QED", because the transmon capacitor will be much bigger than the wavelength of the bosonic mode, makes it a giant atom. Dokument
Urheberrecht: © Sander Konijnenberg
M.Sc.Arbeit Theoretical study of Hall effect gyrators and circulators in the time domain
Circulators and gyrators are nonreciprocal circuit elements that play an important role in microwave systems. It would be desirable to keep such elements small in size, so it has been proposed to create such devices that use the Hall effect (as opposed to e.g. the Faraday effect which makes for relatively large devices). It has been shown that by coupling leads capacitively to a 2D Hall conductor, lossless circulators and gyrators can be made. The response of such devices has been studied in the frequency domain, but these results cannot be trivially transformed to the time domain. In this report we study the behaviour of Halleffect gyrators and circulators in the time domain. Dokument (PDF)
Urheberrecht: © Susanne RicherM.Sc.Arbeit Perturbative Analysis of TwoQubit Gates on Transmon Qubits
This thesis treats different schemes for twoqubit gates on transmon qubits and their per turbative analysis. The transmon qubit is a superconducting qubit that stands out due to its very low sensitivity to charge noise, leading to high coherence times. However, it is also characterized by its low anharmonicity, making it impossible to neglect the higher transmon levels.
Coupled systems of superconducting qubits and resonators can be treated in cavity QED. In the dispersive regime, where qubit and resonator are far detuned from each other, per turbative methods can be used for the derivation of effective Hamiltonians. Several such methods are presented here, among which the SchriefferWolff transformation results to be the most adequate. Dokument (PDF)
Gruppe Hassler
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M.Sc.Arbeiten
Hexagonal Majorana fermion lattice constructed from topological insulator Josephson junctions
In this thesis, we discuss the realization of a hexagonal Majorana fermion lattice and its thermal transport properties. We analyze the twodimensional Josephson junctions on the surface of topological insulators to obtain topological Majorana wires in the lowenergy regime. Using this description of the wires, we construct trijunctions and derive three distinct topological phases of them, two of which host Majorana bound states. We connect multiple Majorana bound states with topological insulator Josephson junctions to a hexagonal lattice of Majorana fermions. The spectrum of this lattice is calculated, the appearance of edge states is shown, and the scaling behavior of the thermal conductance of the hexagonal Majorana lattice is analyzed. Dokument (PDF)
Urheberrecht: © Steven KimLindblad Equation, Symmetries, and Instabilities in DrivenDissipative Systems
In this thesis, we study drivendissipative systems that can be de scribed by a Lindblad master equation. In particular, we analyze parametrically driven oscillators that exhibit an instability when the driving strength exceeds the damping. In this critical regime, both fluctuations and nonlinearities have to be included for an accurate description of the system. For the degenerate parametric oscilla tor, it has been shown that the longtime dynamics can be described by a universal Liouvillian. This makes the efficient calculation of observables, such as the photon current, possible. To determine the longtime dynamics, we provide a method to solve the Lindblad equation, which makes the separation of timescales possible. This is used to derive the effective model for the nondegenerate parametric os cillator, and we analyze the resulting statistics of radiation. Additionally, we discuss how symmetries of the Lindblad equation are described. Dokument (PDF)
Urheberrecht: © Alexander ZiesenLattice Gauge Theoretic Analysis of Topological Ordering in the Majorana Toric Code
In this thesis, we consider a two dimensional square lattice of mesoscopic superconducting islands carrying four Majorana zero modes (MZM) each. We consider the islands to form an array of Josephson junctions, where the MZM allow for additional interisland single electron transfer. This model is known to realize topological order in the form of Kitaev's toric code. With a calculation of the effective Hamiltonian, we prove that the presence of charge2e Josephson tunneling has a stabilizing effect on the toric code gap. The goal of this thesis is to investigate the signatures of topological ordering. To this end, we introduce a duality mapping of the MZM to spins yielding a lattice gauge theory and shift the focus from the matter to the gauge perspective. In this form, we can utilize the equal time formulation of the FredenhagenMarcu order parameter, a generalized Wilson loop, to detect the topological signatures and give an intuitive picture of (open) loop condensation to understand the topological phase
transition. Dokument (PDF)
Dual Shapiro steps of a phaseslip junction in the presence of a parasitic capacitance
This thesis investigates the emergence of dual Shapiro steps in the IVcurve of a single Josephson junction in the phaseslip regime. In particular, we analyze the detrimental effect of the parasitic capacitance between the biasing lines and how it can be remedied by an onchip superinductance. We obtain an explicit analytical expression for the height of dual Shapiro steps as a function of the ratio of the parasitic capacitance to the superinductance. Using this result, we provide a quantitative estimate of the dual Shapiro step height. Our calculations reveal that even in the presence of a parasitic capacitance it should be possible to observe dual Shapiro steps with realistic experimental parameters. Dokument (PDF)
Urheberrecht: © Florian VennAlgebraic Methods for the 1D Schrödinger Equation
We discuss algebraic methods to obtain exact results about the eigenvalue spectrum of the one dimensional Schrödinger equation. We focus on degeneracies in the spectrum and eigenvalues that are exactly solvable. The central object in our discussion is supersymmetry. First, we give an introduction to the description of problems using superpotentials. We present insights that can be obtained from the supersymmetric structure, in particular the degeneracies between bosonic and fermionic states and that the groundstate admits an algebraic solution. We use these insights to study the double sine potential. By tuning the double sine potential away from the point where it can be described using supersymmetry, we find an extension of supersymmetry that is related to a class of problems for which multiple eigenstates admit algebraic solutions. Next, we prove, for a subclass of these problems, that a degenerate partner state exists for almost all eigenstates. Finally, we highlight that the class of periodic problems with more than one exactly solvable eigenvalue is not limited to the double sine potential. Dokument (PDF)
Urheberrecht: © Elias WalterInfluence of chiral symmetry on electron scattering at disordered graphene boundaries
In this thesis, we study scattering processes at disordered graphene boundaries. In particular, we investigate how the chiral symmetry of quasiparticles in graphene influences diffusive scattering. We find that a boundary that breaks chiral symmetry behaves like a mirror, in the sense that in the long Fermi wavelength limit diffusive scattering is suppressed and incoming electrons are reflected specularly. However, if the disorder on average preserves chiral symmetry, diffusive scattering increases significantly, leading to a breakdown of the mirrorlike behavior. Dokument (PDF)
Urheberrecht: © Daniel OttenSecondOrder Coherence of Microwave Photons Emitted by a Quantum Point Contact
In this work we present a diagrammatic approach to calculate current cumulants for the electron transport through a quantum point contact. We provide compact expressions for cumulants up to and including the third order. Furthermore, fluctuations in the electronic current lead to emitted radiation in the microwave regime. In this context the current cumulants are linked to the photon counting statistics of the microwave field. For this setup, we calculate the Fano factor F and the secondorder coherence function g ^{(2)}(τ). Dokument (PDF)
Urheberrecht: © Dominique DresenQuantum Transport of NonInteracting Electrons in 2D Systems of Arbitrary Geometries
The scattering formalism for describing the trans p ort properties of systems is discussed. We apply the formalism to GaAs and graphene with different geometries and types of disorder. For example, we discuss impedance matching of graphene to outside leads, AharnnovBohm effect in a ring geometry, and how strainfluctuations in graphene manifest themselves in the transport properties. Dokument (PDF)
Urheberrecht: © Sebastian RubbertTuneable Long Range Interactions in an Array of coupled Cooper Pair Boxes
The Kitaev chain emulating the transverse Ising model can be implemented in an array of superconducting islands with semiconducting nanowires. In this thesis, we will show that adding additional capacitances to the system implements a longrange interaction between the Ising degrees of freedom. Dokument (PDF)
B.Sc.Arbeiten
 Jonas Völler: Stabilizing Josephson radiation in the presence of thermal noise
 Emily Büschges: Electronhole excitations in a ring driven by a timedependent AharonovBohm flux
 Maximilian Hauke: Effects of noise on dual Shapiro steps
 Apostolos Siskou: Fluctuation of radiation emission near a parametric instability
 Fynn Janssen: Period tripling in a parametrically driven Duffingoscillator
 Yves Rottstaedt: Supercurrent diode effect
 Steven Kim: Single mode Lindblad description of the parametric instability
 Leona Rodenkirchen: Different Approaches to Stochastic Quantization in OneDimensional Processes
 David Scheer: Escape from a metastable state due to thermal fluctuations described by path integrals
 Mats Volmer: Edge states of Chern insulators in various geometries
 Jakob Stubenrauch: Effective Hamiltonians for Linear Environments
 Sebastian Miles: Application of the Matrix Numerov Method to Periodic or Singular Potentials in the 1D Schrödinger Equation
 Ole Jasper: Stability of the MatrixNumerov Method for Solving the 1D Schrödinger Equation
 Julio Magdalena: Scattering of electrons off strain fluctuations in graphene
 Timon Vaas: Semiclassical Green’s function of a BCS superconductor in a half space
 Florian Venn: Quantum Oscillations in Graphene Rings
 Uta Meyer: Obstruction of Information Transfer by Locality in Majorana Systems
 Lisa Arndt: TimeScales of Charge Relaxation in a Superconducting Island via an Inductive Shunt
 Jonas Stapmanns: Universal conductance peak in the transport of electrons through a floating topological superconductor
 Felix Stamm: Modeling of a nanomechanical oscillator with adiabatic correction to scattering theory
 Daniel Otten: Magnetic Impurity Coupled to Helical Edge States
 Mauricio Cattaneo: NonAbelian exchange statistics of Majorana fermions
 Christoph Baumann: Transport properties of a disordered chain of Majorana fermions
Gruppe Müller
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B.Sc.Arbeiten
 Max Oberländer: Schrödinger Cat States in Ion Traps
 Leon Bohnmann: Quantum Error Correction of Computational Errors and Qubit Loss
Gruppe Terhal
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B.Sc.Arbeiten

Nikolas Breuckmann:Quantum Subsystem Codes: Their Theory and Use

Andres Goens: Code Space Dimension of TranslationallyInvariant Qubit Stabilizer Codes

Daniel Weigand: Entanglement Entropy of 1D Noninteracting Fermionic Systems

Tobias Hoelzer: Study of [[4,2,2]]concatenated toric code for a scalable circuitQED architecture. C++ code

Friederike Metz: SpaceTime CircuittoHamiltonian Construction Applied to a MERA Circuit

Rene Kempen: A Transpose Channel Approach to Approximate Quantum Error Correction

Timo Simnacher: Nonlocal Boxes: Theory & Implementation in Minecraft

Dominik Michels: The Sign Problem in Boson Sampling.

Jonathan Conrad: Parity Check Schedules for Hyperbolic Surface Codes

Eva Fluck: Time evolution with randomized approximate Trotter expansion
M.Sc. Project Deterministic Encoding of a Qubit in a Cavity Mode using Phase Estimation
In this thesis, several deterministic protocols are proposed and analyzed that use circuit quantum electrodynamics to approximately encode a qubit in an oscillator by dispersively coupling a transmon qubit to a microwave cavity mode.
Urheberrecht: © Yang WangM.Sc. Project Quantum Error Correction with the GKP code and Concatenation with stabilizer codes
In this thesis, we propose a method to utilize all the information contained in the continuous shifts for quantum error correction, which improves over simply mapping a GKPencoded qubit to a normal qubit.
Urheberrecht: © Nikolas BreuckmannM.Sc. Project From quantum circuits to Hamiltonians: analysis of a multitime construction for QMA
This thesis lies in the area of quantum complexity theory. It proves the QMAcompleteness of a class of 2D interacting fermion Hamiltonians.
Dokument (PDF)
M.Sc. Project Improving Transmon Qubit Readout Using Squeezed Radiation
The goal of this project has been to analyze whether the use of squeezing in a MachZehnder interferometer can give rise to a faster, high fidelity, measurement of superconducting transmon qubits.
Dokument (PDF)